Solutions Set-1

Q1. 0.50 mol of glucose (non-electrolyte) is dissolved in 1.00 kg of water. Using $\Delta T_f = K_f\,m$ and $m=\dfrac{\text{moles of solute}}{\text{kg of solvent}}$, and given $K_f=1.86\ \text{K kg mol}^{-1}$ for water, the freezing point of the solution (in $^\circ\text{C}$) is:

Q2. For an ideal binary solution at $300\ \text{K}$, the vapour pressures of pure components are $P_A^0=400\ \text{Torr}$ and $P_B^0=200\ \text{Torr}$. If the mole fraction of A in the liquid is $x_A=0.25$, calculate the mole fraction of A in the vapour phase $y_A$ (use $p_A=x_AP_A^0$ and $y_A=\dfrac{p_A}{p_{\text{total}}}$).

Q3. A $0.010\ \text{M}$ aqueous solution of $\mathrm{MgCl_2}$ at $25^\circ\mathrm{C}$ exhibits an osmotic pressure of $0.600\ \text{atm}$. Assuming $\mathrm{MgCl_2}\rightarrow \mathrm{Mg^{2+}+2Cl^-}$ with degree of dissociation $\alpha$, and using $\pi=i M R T$ where $i=1+2\alpha$ for $\mathrm{MgCl_2}$ and $R=0.0821\ \text{L atm mol}^{-1}\text{K}^{-1}$, the value of $\alpha$ is approximately:

Q4. Two dilute solutions at the same temperature are prepared by dissolving solutes in equal masses of the same solvent; both show the same lowering of solvent vapour pressure $\Delta p$. Solution I contains a non‑volatile nonelectrolyte. Solution II contains NaCl which is fully dissociated. Using $\Delta p\approx x_{\text{solute}}P^0$ and $\pi=i M R T$, which statement about their osmotic pressures $\pi_I$ and $\pi_{II}$ is correct?

Q5. Five-point-zero-zero grams of a volatile solute $B$ is dissolved in $90.0\ \text{g}$ of benzene (molar mass $=78.0\ \text{g mol}^{-1}$). At the temperature of measurement $P_{\text{benzene}}^0=100.0\ \text{Torr}$ and $P_B^0=50.0\ \text{Torr}$; the vapour pressure of the solution is $94.0\ \text{Torr}$. Using $p_{\text{total}}=x_{\text{benzene}}P_{\text{benzene}}^0+x_BP_B^0$ with $x_i=\dfrac{n_i}{n_{\text{total}}}$, the molar mass of $B$ (in g mol$^{-1}$) is approximately:

Q6. A solution is prepared by dissolving $18\ \mathrm{g}$ of glucose ($\mathrm{C_6H_{12}O_6}$, $M=180\ \mathrm{g\,mol^{-1}}$) in $162\ \mathrm{g}$ of water. The molality of the resulting solution is:

Q7. An ideal binary solution contains $1$ mole of volatile liquid A and $3$ moles of volatile liquid B. Vapour pressures of the pure components at the temperature are $P_A^\circ=200\ \text{mmHg}$ and $P_B^\circ=600\ \text{mmHg}$. Using Raoult's law, the mole fraction of A in the vapour phase in equilibrium with this solution is:

Q8. A polymer sample of mass $2.00\ \mathrm{g}$ is dissolved to make $0.250\ \mathrm{L}$ of solution at $298\ \mathrm{K}$ and the osmotic pressure measured is $0.0822\ \mathrm{atm}$. Using $R=0.08206\ \mathrm{L\,atm\,mol^{-1}\,K^{-1}}$, the approximate molar mass of the polymer is:

Q9. $0.200\ \mathrm{mol}$ of $\mathrm{CaCl_2}$ is dissolved in $1.000\ \mathrm{kg}$ of water. Assume complete dissociation into three ions and ideal behaviour. If the vapour pressure of pure water at this temperature is $23.76\ \mathrm{mmHg}$, the vapour pressure of the solution (using Raoult's law with mole-fraction approximation) is approximately:

Q10. A non-electrolyte compound with true molar mass $150\ \mathrm{g\,mol^{-1}}$ dimerizes in benzene according to $2X\rightleftharpoons X_2$. A colligative measurement gives an apparent molar mass of $225\ \mathrm{g\,mol^{-1}}$. The fraction of molecules that have dimerized (degree of association $\alpha$) is: